摘要
在乘群k*中,希尔伯特定义了一种两个元素a,b之间的运算(a,b),称为希尔伯特符号,在此我们利用已经推得的(a,b)简单运算公式及性质,采用指数α,β,仅由它们的模2的剩余类决定这一特性,将α,β分成3种情形,根据乘群k*的性质、Legendre符号性质及p进方程的理论,对它的计算进行讨论.
In the multiplicative group, Hilbert definites an operation between a and b, and it denotes by the so-called Hilbert symbol ( a, b ). In this paper , we will deduce the calculating formulas of Hilbert symbol ( a, b ) by using some results in the following: the characters of the exponents α and β are decided only by their residue class modul 2, the properties of multiplicative group and Legendre' s symbol, the theories of p-adic equation and so forth.
出处
《沈阳化工学院学报》
2007年第3期235-237,共3页
Journal of Shenyang Institute of Chemical Technolgy
关键词
希尔伯特符号
乘群
非平凡解
P进单位元素群
Hilbert symbol
multiplicative group
non-trivial solution
group of p-adic units